On the origin of the Vogel-Fulcher-Tammann law in the thermo-responsive shape memory effect of amorphous polymers

All amorphous shape memory polymers (SMPs) are featured by their relaxation behavior above and below the switching transition temperature (TSW). Above TSW, the glass transition and secondary transition merge together, resulting in the cooperative (α) movement in polymer macromolecules. Below TSW, movement is non-cooperative (β). In this study, three thermodynamic constitutive frameworks for the shape recovery behavior in amorphous SMPs are proposed based on the Arrhenius, Vogel-Fulcher-Tammann (VFT) and Bässler laws, respectively, and incorporated with parameters (stress, strain and relaxation time) as functions of temperature. The relaxation times of α and β movements satisfy the VFT and Arrhenius laws, respectively. The simulation is compared with the available experimental results reported in the literature for verification. The VFT law is found to be better than the other models, and is able to provide an accurate prediction for the temperature dependent relaxation behavior, from the Arrhenius behavior below, to the Williams-Landel-Ferry behavior above TSW.